Why Charges Have Mass?

The force $F_\rho$ to affect a change in $\psi$ is given by,

$F_\rho=-\cfrac{\partial\,\psi}{\partial\,x}$

This force act against the system and results in work done that is equal to a change in energy $\psi$.  So, the resistance exerted by the system of a solitary particle on an external agent is given by,

$F_i=-F_\rho=\cfrac{\partial\,\psi}{\partial\,x}$

where $F_i$ is the force exerted by the particle on an external agent.  So,

$F_i=-F_{\rho}=-i\sqrt { 2{ mc^{ 2 } } }\,G.tanh\left( \cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  } (x-x_z) \right)$

The following diagram shows the interaction between two monopoles of positive $F_i$, ie (-$F_\rho$)

The concentration of $\psi$ between the two particles pushes them apart.  And their interaction is thus repulsive.

In a similar way, the diagram below shows the interaction between two monopoles of $-F_i$, ie (+$F_\rho$)

The depletion of $\psi$ between the two particles pulls them together.  And their interaction is thus attractive.

Both diagrams show $F_{\rho}$, the force developed in previous posts, from an external agent affecting a change in $\psi$ around the particle.  Strictly speaking the force due to the particles are,

And the interaction of two dissimilar particles is,

If the interaction of two positive $F_i$ is that of charges (repulsive, like charges repel) and the interaction of two $-F_i$ is that of gravity particle (attractive, two masses attract), then the interaction of $F_i$ and $-F_i$ shown above, is attractive as though the charge has mass; the interaction between two masses is attractive.

If the interaction of $+F_i$ is that of negative charges, then along the negative $t_c$ time dimension we have positive charges.  Similarly, along $-t_g$ time dimension, anti-mass particles.

Negative and positive charges are matter/anti-matter pair, and mass and anti-mass are similarly matter/anti-matter pair.